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Gaussian measures on linear spaces. (English) Zbl 0881.28009

The article under review is an impressive survey of the modern theory of Gaussian measures on locally convex spaces with a particular attention to Radon-Gaussian measures. Many classical results of the linear theory are presented with detailed proofs. In particular, the author discusses measurable linear functionals and operators, zero-one laws, equivalence/singularity, etc. One of the chapters is devoted to nonlinear problems. Gaussian-Sobolev classes, elements of the Malliavin Calculus, nonlinear transformations, and Gaussian capacities are discussed also (however, mostly without proofs). The survey contains an extensive bibliography (about 600 items). A more detailed exposition of the same subject is given in the author’s recent book “Gaussian measures”, Moscow: Nauka, Fizmatlit (1997).

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46G12 Measures and integration on abstract linear spaces
60H07 Stochastic calculus of variations and the Malliavin calculus
60B11 Probability theory on linear topological spaces
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References:

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